He is in error about one thing. He says you can’t miss at X distance (short). Yes you can, and if you do most of time the reason is as detailed here.
Cops are trained wrong. Just like Leatham says, precision shooting and rapid fire are different animals.
Now I am not 100 in agreement with Leatham. But since I know you are more apt to listen to him….
If you train his way, you will improve.
You need to train for both though, precision and speed.